An arithmetic characterization of decomposition methods in Banach spaces similar to Pełczyńsk's decomposition method

• Autorzy: Galego E. M.
• Języki publikacji: EN

Abstrakty

EN

Inspired by Pełczyński's decomposition method in Banach spaces, we introduce the notion of Schroeder-Bernstein quadruples for Banach spaces. Then we use some Banach spaces constructed by W. T. Gowers and B. Maurey in 1997 to characterize them.

Słowa kluczowe

EN

Pełczyński's decomposition method; Schroeder-Bernstein problem; Banach spaces

PL

zagadnienie Schroedera-Bernsteina; przestrzeń Banacha

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: Vol. 52, nr 3
• Strony: 273--282
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Galego E. M.

Bibliografia

• [1] P. G. Casazza, The Schroeder-Bernstein property of Banach space, in: Contemp. Math. 85, Amer. Math. Soc., 1989, 61-77.
• [2] E. M. Galego, How to generate new Banach spaces non-isomorphic to their cartesian squares, Bull. Polish Acad. Sci. Math. 47 (1999), 21-25.
• [3] -, Banach spaces complemented in each other without isomorphic finite sums, ibid. 50 (2002), 1-9.
• [4] -, On solutions to the Schroeder-Bernstein problem for Banach spaces, Arch. Math. (Basel) 74 (2002), 299-307.
• [5] W. T. Gowers, A solution to the Schroeder-Bernstein problem for Banach space, preliminary version (unpublished).
• [6] -, A solution to the Schroeder-Bernstein problem for Banach space, Bull. London Math. Soc. 28 (1996), 297-304.
• [7] W. T. Gowers and B. Maurey, Banach spaces with small spaces of operators, Math. Ann. 307 (1997), 543-568.